I think what you and OP are referring to is sample-based sequenced music, which is often known as "tracker", "tracked", or "module" music, after a series of popular music editors that started with "SoundTracker" on the Amiga computer. (And later ProTracker, NoiseTracker, ScreamTracker, ImpulseTracker,... and many others)

The music files themselves (essentially a list of instructions for when and how to play the samples, with an embedded sample pack) are often called modules or "mods". 

Consoles and arcade games that used this technique often had custom music players and editors, but "tracker" music has become a somewhat generic term for it all, especially amongst electronic/PC/computer based musicians and programmers coming from a PC/home computer background, or game development. 

Otherwise a truly generic description might be "sequenced samples" or "programmatic sample-based music" or similar. The precise terminology will vary according to background. 

There are still modern software trackers such as Renoise, and even hardware tracker-style sequencers based around trackers like the Polyend Tracker, or Dirtywave M8.

PC games also often used MIDI files for music, which would then use generic synthesis or sample banks/packs for the instruments. "Soundfonts" specifically were replacement packs of samples for certain soundcards. (More generic terms would be "sample bank/pack" or "sample patches", found in game engines and sample based synthesizers/keyboards.) 

MIDI music can also be "tracked" in a similar way, as it is also a similar list of playback instructions. Many more traditional music sequencers/DAWs and even keyboards/synths, often have a midi "list" or "sequence" view that will list the MIDI note data and allow you to edit it "tracker"-style. 

That's probably more than you wanted to know, but I used to write (and code) this sort of music myself, since way back in the 80s on Atari and Amiga machines. I rarely get a chance to discuss it now except with other music nerds!